cp's OEIS Frontend

From M. F. Hasler and Farideh Firoozbakht, Apr 08 2010: (Start)

Theorem: If p is a term of this sequence and p-1 is a t-perfect number then for each positive integer k, x=p^k is a solution to the equation sigma(phi(x)) = t*(x-1).

Proof: sigma(phi(x)) = sigma(phi(p^k)) = sigma((p-1)*p^(k-1)) = sigma(p-1)*sigma(p^(k-1)) = t*(p-1)*(p^k-1)/(p-1) = t*(p^k-1) = t*(x-1). (End)

A subsequence of A093034. If p is a term of this sequence then for each positive integer k, x=p^k is a solution for the equation sigma(phi(x))=4(x-1). See comment lines of the sequence A093034.

Primes of the form 1+A046061(n). A subsequence of A093034. This sequence has only 8 terms. a(5)=1+A046061(76),a(6)=1+A046061(79),

a(7)=1+A046061(204) and a(8)=1+A046061(209).

If p is a term of this sequence then for each positive integer k, x=p^k is a solution for the equation sigma(phi(x))=6(x-1). See comment lines of the sequence A093034.

A subsequence of A093034.

If p is a term of this sequence then for each positive integer k, x=p^k

is a solution for the equation sigma(phi(x))=3(x-1). See comment lines of

the sequence A093034.